KöMaL 2019 B5044

Let $D$ be a point in the interior of side $AB$ in triangle $ABC$, and $E$ be a point in the interior of side $AC$. The intersection of line segments $BE$ and $CD$ is $M$. Let $x$ denote the area of triangle $BCM$, and let $y$ denote the area of triangle $EDM$. Prove that $T_{ABC}\ge x \frac{\sqrt x+\sqrt y}{\sqrt x-\sqrt y}$.